The parameters are in the order correlation, row thresholds (of which there
are 6), column thresholds (of which there are 4), and at this point in the
maximization of the likelihood the first row threshold (-2.20343446037221)
is *above* the second threshold (-2.2163627792244), causing pmvnorm() to
complain. This can happen when the problem is ill-conditioned, since optim()
doesn't constrain the order of the thresholds.

There are only two observations in the first row, two in the second row, and
one in the first column. You're expecting a lot out of ML to get estimates
of the first couple of thresholds for rows and the first for columns.

One approach would be to eliminate one or more sparse rows or columns; e.g.,

That's because the two-step estimator estimates the thresholds from the
marginal distributions of the variables rather than from their joint
distribution.

So, is this a bug or a feature? I suppose that it's a bug to allow the
thresholds to get out of order, though to constrain the optimization to
prevent that from happening is probably not worth the effort and could cause
some strange results. On the other hand, the error tells you something about
the data, so maybe it's a feature.

I noticed that you posted another version of this question two days before
this one. I apologize for the slow response -- I wasn't able to read my
email for a few days and it's taken me most of today to catch up.

Regards,
John

---- original message -------

Janet Rosenbaum jrosenba at rand.org
Thu Aug 24 00:41:16 CEST 2006

Hi.

Does anyone know whether the following error is a result of a bug or a
feature?

I can eliminate the error by making ML=F, but I would like to see the
values of the cut-points and their variance. Is there anything that I
can do?